The structure of ecological state transitions: Amplification, synchronization, and constraints in responses to environmental change

Effects of environmental change may be either amplified and facilitated, or constrained, by the network of state-changes in ecological systems. Network structure affects system response independently of the dynamics of the individual subsystems. Ecological responses were represented as state-and-transition models (STMs), and analyzed as mathematical graphs. Three metrics were applied that reflect: (1) the extent to which environmental change is amplified or filtered by state transitions; (2) network synchronizability and the rate of propagation of state changes; and (3) the extent of system structural constraints to the spatial propagation of state transitions. These were determined for seven archetypal graph structures representing common forms of connectivity in ecological networks, and linked to distinct modes of ecological change. Radiation-type structures are the least synchronized and most constrained patterns, with the most limited amplification, followed by other low-connectivity patterns such as those associated with monotonic succession. The maximum-connectivity rigid polygon structure (any state can transition to any other) has the strongest amplification and synchronization and least constraints. Structural constraints to change propagation are most sensitive to increasing numbers of transitions for a given number of states, and synchronization also increases at least linearly with the number of links. Amplification, however, does not increases as rapidly; as long as a graph is connected, increasing the number of links does not proportionally increase it. Because the more densely connected structures have much higher synchronization than other patterns, and fewer constraints on change propagation, environments characterized by these types of STMs may be prone to rapid, complex transitions in response to environmental changes. STMs for rangelands in two regions of Texas show that the rigid polygon structure is very common. If this phenomenon is more general, it suggests that relatively abrupt landscape reorganizations may be more likely than more orderly successions of change along environmental gradients. This analysis shows that identification of STMs and their network structure is useful for recognizing environments at higher risk for complex reorganization, and for identification of management actions to either retard or facilitate propagation of state changes.